The random access procedure of E-UTRAN resembles that of WCDMA (Wideband Code Division Multiple Access). In both systems, in a first step a user equipment (UE) transmits a preamble on an access slot. A number of different preamble sequences have been defined for the UE to select for the preamble transmission. For E-UTRAN, so called Zadoff-Chu sequences have been chosen. The length of a sequence is 839 samples, which means that 838 root sequences are available. Depending on the cell range which defines delay uncertainty, up to 64 cyclically shifted sequences are obtained from a root sequence.
In E-UTRAN FDD (Frequency Division Duplex) system, 64 preamble sequences are allocated for each cell. In order to minimize system information, only a root sequence index u0 and a cyclic shift increment Ncs and a mobility parameter are broadcasted for UEs of a cell. The UEs form a complete set of 64 sequences by determining available cyclic shifts of the sequence u0 and continuing from the consecutive root sequences until the 64 sequences are collected.
This selected sequence allocation system means that it is required to define an order of the root sequences. The ordering should be decided taking into account two issues.
The first issue is that the cubic metric (CM) of the sequences varies depending on the root sequence index. CM is important because it defines the power back-off that is needed for reaching a certain level of adjacent channel interference when a typical nonlinear transmitter of a UE is assumed. When CM is high, UE cannot transmit with as high mean power as in case of low CM. This means that the coverage (i.e. the supportable cell radius) varies depending on the root sequence. Then it would be preferable to order the root sequences according to CM so that the consecutive root sequences (that are allocated to the same cell) would support roughly the same cell size.
The second issue to consider is that a so called sequence restriction scheme may completely deny utilization of a root sequence or at least some of its cyclic shifts. The restriction scheme is needed because of the special properties of the Zadoff-Chu sequences in case of large frequency offsets, and the scheme will be applied in cells where UEs can move with high speeds. In the following, such cells are called high mobility cells, and the other cells, where restrictions are not applied, are called low mobility cells. A mobility parameter of the System Information indicates if the restrictions are in use. The restrictions define a maximum supportable cell size for each root sequence. If the sequences are ordered according to the maximum supportable size of a high mobility cell, the reuse of the sequences can be optimized in presence of both high and low mobility cells: Those root sequences that are not available in high mobility cells of a certain size form a set of consecutive sequences that can be effectively allocated for low mobility cells.
The two ordering systems, according to CM and according to the maximum size of high mobility cell, are contradicting: sequences with nearly equal CM may support completely different sizes of high mobility cell.